What is the preferred network connection?

The network router, the NAS and other network device directly attached to router using Ethernet cable can be quite noisy. If the streamer is attached to the router using Ethernet cable then the noise can easily been transmitted to the streamer as it is a physical link. The regular CE, FCC and other EMC standard only guarantee the device will work stably, but when are talking about sound quality, we are actually talking about the EMI noise that is 1/1000 of EMC's standard, so it affect a lot. That's why audiophile say different NAS, or different routers sound different.

The Ethernet cable is a big trouble, it runs long and can pickup low frequency noise which there is just no way to get rid of. Those noise will transfer into low frequency jitter at low frequency even more difficult to get rid of. Low frequency jitter affects sound quality a lot.

The WiFi sound better if:

The engineer who in charge of design the streamer knows how to design the WiFi module right. The 'right' means the WiFi module will not create noise that can be picked up by other audio circuit of those which directly sharing same ground circuit;

The WiFi signal between streamer and router is strong and stable. If you have a poor WiFi signal between streamer and the music server, the WiFi protocol will try to fetch the data again and again due to large error rate (Yes, we use TCP to transfer music data which has error correction policy). If there are too many errors, that add quite a lot of work for the WiFi module and it will also add additional load to processor which potentially generate more EMI noise and affect audio circuit.